A007150 2-part of number of tournaments on n nodes.

0, 0, 1, 2, 2, 3, 3, 5, 4, 6, 5, 7, 6, 7, 7, 10, 8, 9, 9, 12, 10, 11, 11, 14, 12, 14, 13, 15, 14, 17, 15, 19, 16, 20, 17, 19, 18, 19, 19, 26, 20, 22, 21, 23, 22, 23, 23, 30, 24, 26, 25, 28, 26, 27, 27, 30, 28, 30, 29, 33, 30, 31, 31, 35, 32, 34, 33, 38, 34, 37, 35, 38, 36, 38, 37, 39

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..141
• Steven C. Cater and Robert W. Robinson, Exponents of 2 in the numbers of unlabeled graphs and tournaments, Congressus Numerantium, 82 (1991), pp. 139-155.
• Steven C. Cater and Robert W. Robinson, Exponents of 2 in the numbers of unlabeled graphs and tournaments, Preprint. (Annotated scanned copy)
• Index entries for sequences related to tournaments

Crossrefs

Power of 2 dividing A000568(n). Cf. A007814.

Programs

Mathematica

A000568 = Cases[Import["https://oeis.org/A000568/b000568.txt", "Table"], {, }][[All, 2]];
IntegerExponent[#, 2]& /@ A000568 // Rest (* Jean-François Alcover, Jan 06 2020 *)

Python

from itertools import product
from math import prod, factorial, gcd
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A007150(n): return (~(m:=int(sum(Fraction(1<<(sum(p[r]*p[s]*gcd(r,s) for r,s in product(p.keys(),repeat=2))-sum(p.values())>>1),prod(q**p[q]*factorial(p[q]) for q in p)) for p in partitions(n) if all(q&1 for q in p)))) & m-1).bit_length() # Chai Wah Wu, Jul 01 2024

Formula

a(n) = A007814(A000568(n)). - Michel Marcus, Jan 06 2020

Extensions

More terms from A000568 by Jean-François Alcover, Jan 06 2020